Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

I'm afraid that this is not one of my favourite Millay poems - much as I
usually love her work, I feel that she has failed to do the subject justice
(or, perhaps, that the matter doesn't really suit her style; either way, it
lacks the feel of her really great pieces).
However, it does fit very neatly into the theme, and is worth a read, if as
much for its symbolism as for the actual poem. The comparison of
mathematical insight to a divine revelation, for instance, is a rather
standard image, but one that springs naturally to mind, for reasons not too
hard to see - most of the universe can be explained using a judicious
combination of mathematics and religion :).
Also very interesting is the parallel drawn between the transcendence into
beauty and the transition from sound to light. Mathematics seems to have
associated with it a certain abstract purity that finds its closest
reflection in our images of space and light, or perhaps light comes closest
to the geometric ideal of a straight line (one of the cornerstones of
practically all mathematics, and certainly one of the key tools in its
development). And of course, there is the obvious reference back to the
light/revelation image,
The basic form is Petrarchan, with a slightly unusual rhyme scheme in the
sestet (though see http://www.sonnets.org/basicforms.htm - the sestet had a
pretty flexible rhyme scheme). Notable is the fairly heavy use of
alliteration, which adds to the poem's somewhat 'weighty' feel.
As an afterthought, this heaviness is probably my main objection to the poem
- Millay has tried to capture both the majesty and the ethereal nature of
mathematics, but has associated with the former a weight that is quite at
variance with the latter.
Note:
Euclid is probably one of the most famous, and certainly one of the most
influential mathematicians of all time; his 'Elements', a massive
compilation of the mathematical knowledge of time time revolutionised the
field, setting the standard for rigour that even now characterises
mathematics.
Almost from the time of its writing and lasting almost to the present, the
Elements has exerted a continuous and major influence on human affairs. It
was the primary source of geometric reasoning, theorems, and methods at
least until the advent of non-Euclidean geometry in the 19th century. It
is sometimes said that, next to the Bible, the Elements may be the most
translated, published, and studied of all the books produced in the
Western world. Euclid may not have been a first-class mathematician. He
certainly was, however, a first-class teacher of mathematics, inasmuch as
his textbook has remained in use practically unchanged for more than 2,000
years.
-- EB
I could go on about Euclid for several pages; however, inasmuch as this is a
poetry list I'll leave you to explore the several excellent books and
webpages about him and his work yourselves <g>.
Links:
Here's a biography of Millay: poem #34
And two of Euclid:
[broken link] http://www.treasure-troves.com/bios/Euclid.html
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html
And here is one of his more celebrated theorems - 'beauty bare' indeed!
[broken link] http://www.math.umd.edu/~krc/numbers/infitude.html
-martin

I think you're driving with twos wheels off the road. That's actually a comment about deconstruction criticism, but it suits yours here. Maybe you're uncomfortable with Millay's actual point and prefer not to find it. Millay is not a poet whose meaning one has to "FEEL." So, the fact that this poem is hard to grasp and leaves the reader little apparent choice but to "feel" what it means IS a problem. But my response is to go on trying to analyze it until I've actually fully understood it and to bite my tongue until I've done that.

I have adored this poem since first reading it over 30 years ago. Most of us will never have complete and intuitive insight into beauty or anything else, not through mathematics, not through music. We adumbrate what true genius grasps, collates, and conveys through imperfect material models. We contemplate from without, satisfied to perceive and admire something which cannot approximate what was experienced at the source. The notes on the page cannot contain what Chopin heard, the most sublime architectural forms are a flawed reflection of the undrawn geometry of straight line and absolute point, the asymptote receding into eternity. In this temple the columns uphold the sky perfectly, the scale without comma, the year perfectly divisible.

Folks, have none of you thought about this poem as a rebuke to "Ode to a Grecian Urn?"

I'm a scientist/applied mathematician and I read it very clearly that way. Doesn't "let all those who prate of beauty hold their peace" directly slam Keats and many others ... through the Byron/Ruskin appreciations onward?

Similarly I see "Euclid" as a subtle dig at "Grecian," and also wonder what background Edna had in math and science (why "Euclid alone..."), although Euclid was the acme of math for many in her generation, those never going on to calculus etc.

Formal geometry is "bare" ... very 'simple,' harsh, abstract and pure, unadorned by artifice. Even more to the point it is independent of taste, and in principle universally accessible. Alien intelligences would arrive at Euclidean geometry.

It is anti-poetry in most regards, another irony here and one I think Edna is playing on.

Dear Anonymous,I am also a scientist/mathematician who reads poetry (I thought I was the only one!) and I also wondered what background Edna had in mathematics and why Euclid was the only one who got to see Beauty in the Buff. However, even if you are correct that Edna was taking a poke at Keats, her poke took the form of an argument, in a sense saying, "no, you're wrong, real beauty is deeper than mere appearance (i.e. the sort of reality math deals with). Your comment makes it sound as if her poem was *only* a 'rebuke'. But I think that she also had her own point to make. Also, sadly Euclid never got to see the ultimately beautiful equation: e^(i*pi) + 1 = 0.

I was searching for more details about Euclid (for my wife, as she is studying to be teacher in Mathematics). Thank you for the wonderful poem and each of your comments. Internet is amazing, day-by-day.....

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